Practically identical solutions have been submitted by Leo Giugiuc and Siddig Awad Siddig. After an initial step, the problem reduces to a telescoping product.

The basic step is the observation known from the beginning calculus that, for all real $x,$ $\displaystyle\cos x\ge 1-\frac{x^{2}}{2},$ with equality only at $x=0.$ On the other hand, for the double argument, $\cos 2x=2\cos ^{2}x-1,$ implying that